In phase wrapped data, values are phases in the range of -.pi. to .pi. and correspond to unwrapped values which are an integer multiple of 2.pi. plus the corresponding phase values of the phase wrapped data. Stated mathematically, the unknown unwrapped function (.phi.) is wrapped into the interval (-.pi., .pi.) by the operation: EQU .PSI.(t)=.phi.(t)+2.pi.k(t)
in which k(t) is an integer that forces EQU -.pi.&lt;.PSI.(t).ltoreq..pi.
Phase unwrapping is converting the phase wrapped data into unwrapped data.
Phase unwrapping is an important step in topographical mapping of terrain because one of the preferred methods of mapping terrain elevation data is by means of interferometer synthetic aperture radar (IFSAR) measurements and the terrain elevation measurements obtained by IFSAR are phase wrapped values. Phase unwrapping is also used in other applications, such as wave front distortion and adaptive optics, the degree of magnetic field homogeneity in the water/fat separation of magnetic resonance imaging, and the relationship between the object phase and its bi-spectrum phase in astronomical imaging. The present invention is described in terms of its application to IFSAR, but the concept can be used in other applications as well.
Despite the importance of IFSAR for topographical mapping, the actual process of phase unwrapping is usually undertaken or supervised by a phase unwrapping scientist or engineer rather than a topographic user. The need for the phase unwrapping scientist or engineer to be involved in a phase unwrapping process results from the fact that there is no technique or system available which will automatically unwrap the phase wrapped data without intervention by an expert in phase unwrapping. There exist a large number of phase unwrapping algorithms, each with its own strength and weaknesses, but none of the algorithms can be used in a stand alone fashion by non-experts to process IFSAR data. In order to properly achieve the phase unwrapping, intervention by a phase unwrapping expert is required to adjust inconsistencies, to search for regions of incorrectly unwrapped phase or to chose a different algorithm for reprocessing. The only commercial product that performs phase unwrapping of IFSAR data is the Earth View.TM. IFSAR Software by PCI and Atlanta Scientific. The phase unwrapping step in this product requires human editing of what are called branch cuts and the human editing required is a tedious and time-consuming step. Additional examples of phase unwrapping is described in the text "Two-dimensional Phase Unwrapping: Theory, Algorithms, and Software", by D. C. Ghiglia and M. D. Pritt, published by John Wiley & Sons, New York, 1998. This text describes software for eight phase unwrapping algorithms, but a phase unwrapping expert is nevertheless required to evaluate the results and adjust algorithm parameters or to choose another algorithm should one algorithm fail on a given data set.
There is no phase unwrapping algorithm or system available in the prior art that is reliable and accurate enough to be used on a routine basis by non-experts. As a result, important applications like IFSAR processing still require a phase unwrapping expert to process the data. In particular, the lack of automatic phase unwrapping algorithm could adversely impact the NASA space shuttle mission to be launched in 1999 to map the topography of the entire earth.